168k views
4 votes
Describe the transformation from the parent function f(x) = x³ to the function g(x) = (x + 5)³.

User Reisclef
by
7.8k points

1 Answer

4 votes

Final answer:

The function g(x) = (x + 5)³ represents a horizontal translation of the parent function f(x) = x³, shifting it 5 units to the left without any other transformations such as stretching or reflecting.

Step-by-step explanation:

The transformation from the parent function f(x) = x³ to the function g(x) = (x + 5)³ is a horizontal translation. In general, if we have a function f(x) and we create a new function g(x) = f(x - d), this represents a translation of the graph of f(x) d units to the right. Conversely, if we have g(x) = f(x + d), this represents a translation d units to the left. Therefore, the function g(x) = (x + 5)³ is the cube function shifted 5 units to the left. There are no other transformations such as stretching, shrinking, or reflecting over any axis in this particular transformation.

User Ameena
by
9.2k points

No related questions found